Theorems · Theorem · order theory
isSublattice_latticeClosure
∀ {α : Type u_3} [inst : Lattice α] {s : Set α}, IsSublattice (latticeClosure s)- Defined in
- Mathlib.Order.SupClosed
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Lattice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setstatement and proof · cited by 53,352
- Latticestatement and proof · cited by 916
- ClosureOperatorstatement · cited by 371
- IsSublatticestatement · cited by 28
- latticeClosurestatement and proof · cited by 24
- ClosureOperator.isClosed_closureproof · cited by 15
Cited by5
Results whose statement or proof uses this declaration.
- four_functions_theoremproof · cited by 3
- supClosure_infClosureproof · cited by 2
- latticeClosure_sup_inf_inductionstatement and proof · cited by 1
- image_latticeClosureproof · cited by 1
- infClosure_supClosureproof · cited by 0